Generalized ABCD propagation for interacting atomic clouds

TL;DR

This paper extends the atom-optical ABCD matrix formalism to include interaction effects in nonlinear matter wave propagation, providing a perturbative approach that aligns well with full nonlinear models and offers new analytical tools for atomic cloud dynamics.

Contribution

It introduces a perturbative extension of the ABCD matrix formalism to account for interactions in nonlinear matter wave propagation, bridging optical methods and atomic physics.

Findings

Extended ABCD formalism agrees with nonlinear wave equation predictions.

Perturbative approach effectively models interaction effects.

Applicable to stability analysis of matter-wave resonators.

Abstract

We present a treatment of the nonlinear matter wave propagation inspired from optical methods, which includes interaction effects within the atom optics equivalent of the aberrationless approximation. The atom-optical ABCD matrix formalism, considered so far for non-interacting clouds, is extended perturbatively beyond the linear regime of propagation. This approach, applied to discuss the stability of a matter-wave resonator involving a free-falling sample, agrees very well with the predictions of the full nonlinear paraxial wave equation. An alternative optical treatment of interaction effects, based on the aberrationless approximation and suitable for cylindrical paraxial beams of uniform linear density, is also adapted for matter waves.